Matric Notes Physics 9th Ch 4 Turning Effect of Forces Long Questions

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Comprehensive Questions

Q.6 Define and explain center of gravity and center of mass?

Ans.(1) Center of gravity:- the point where whole weight of the body appears to act is known as center of gravity.

Explanation:- We known that everybody consists of large number of practical And each particle has a definite weight. Now the sum of weights of all particles is equal to whole weight to the body appears to act is known as center of gravity of that body.

2) Center of mass:- We know that everybody is made of large number of small practical’s which has a definite mass and the masses of all particle makes mass of the body if we apply a force on body and body starts motion. Then the point at which we have applied the force is called center of mass for example center of mass of a meter rod lies at midpoint.

Q.8 What is equilibrium? Also give its conditions?

Ans. Equilibrium:- the state of rest or uniform motion o a body is called equilibrium (or) if a body possess no acceleration then the body is called in equilibrium.

There are two conditions for a body to be in state of equilibrium. They are given below.

1st condition of equilibrium:- According to 1st condition of “A” body will be in state of equilibrium if the sum of forces acting on a body is zero i.e (£F = o) For example a bulb is hanging from the ceiling with the help of a thread then the weight “w” of bulb is acting in downward direction while the tension “T” in thread is acting in upward direction in this case both forces balance each other i.e resultant of both force is equal to zero a result the bulb remains in state of equilibrium.

2nd condition of equilibrium:- According to this condition “a body will be in state of equilibrium if the sum of anti-clock wise torques is equal to the sum clock wise torques “OR” a body will be in equilibrium it the sum of all torques is equal to zero. £T = 0.

A meter rod is shown in figure at which two force “p” εI  ́are acting at points “A” and “B” though the 1st condition is satisfied but it still rotates and body is not in equilibrium. Not get state of equilibrium we soul make clock wise torque equal to anti –clock wise torque then we will get equilibrium.

When there is no change in translation motion of a body then the equilibrium is known translational equilibrium. Of static objects is called static translational equilibrium eg book .the equilibrium is bodies moving with constant velocity is known as dynamic translational equilibrium. If 2nd condition is satisfied on bodies in rotation then equilibrium is known as rotational equilibrium.

Q9 Define and explain couple?

Ans. Couple:- A couple consists of two parallel forces that are equal in magnitude but opposite in direction eg turning of water top turning of door key and turning of car wheel steering wheel.

Explanation:- Suppose a steering wheel of a car is gripped by two hands form two point “A” and “B” as give in figure. When both hands apply forces F1 and F2 of equal magnitude but in opposite direction. Then the wheel begins to rotate. Such forces applied by both hands, whose magnitude is equal but opposite the direction is called couple the shortest distance b/w two couple forces is called “arm of couple.

Q.10 Explains state of equilibrium in detail?

Ans. State of equilibrium (stability) In different states of equilibrium we discuss the stability of an object. That how a body in equilibrium behaves and how it changes the position of center of gravity when it is disturbed by some external force.

(1) Stable state of equilibrium:- If a body comes back to sits initial position after being disturbed then it is called stable state of equilibrium for example when we left a book form one side laying on the table and then leave it the book will come back to its original position. Because when the book is lifted form one side its center of gravity raised from point “C” to “c” and comes back to its original state due torque

produced by its weight. 

(2) Unstable state of equilibrium:- When a body is slightly disturbed and it does not come back to its

original state then it is called unstable state of equilibrium. For example when a pencil in vertical

position is disturbed, then it falls down and does not come back to its original position because be in this

case the C.G becomes lower from point “C” and the line of action of weight is directed outside of pencil

and it falls down.

(3) Neutral state of equilibrium:- When a body is slightly disturbed and its center of gravity neither lowers nor raised from its original position then such a body is called din state of neutral equilibrium. For example we roll a ball on ground. Then its center of gravity remains at its original position but body rolls forward.

Q.1) What are force diagrams? Define like and unlike parallel forces with example.

Answer: Force diagrams: “Since force is a vector quantity so the effect of all forces acting on the object is usually represented by drawing arrows. Such diagrams are known as force diagrams”.

In force diagrams, the objects on which forces are shown is reduced to a dot at its center and the forces acting on the object are represented by arrows pointing away from it.

Example: Consider the figure in which a brick is lying on the table. The forces acting on the brick are represented by arrows. There are two forces acting on the brick; the weight of the brick that is acting downward and the reaction force i.e. normal force due to the table which is pushing the brick upward.

These forces are equal in magnitude and opposite in direction. Such forces are called balanced forces. When an object is acted on by balanced forces, the forces cancel each other’s effect and the object behaves as no force is acting on it.

Like Parallel Forces: “The forces that are parallel to each other and have the same direction are known as like parallel forces”.

Example: When we lift a box with double support we are applying like parallel forces from each support. The force from one support can be greater than the other.

Unlike Parallel Forces: “The forces that are parallel to each other but have opposite directions are known as unlike parallel forces”.

Example: While driving a car the force acting on the steering wheel by both hands are unlike parallel forces as these are parallel but acting in opposite direction.

Q.2) Explain the addition of forces, in connection with head to tail rule.

Answer: Addition of Forces: “The process of obtaining a single force which produces the same effect as produced by a number of forces acting together is known as the addition of forces”.

Rules for the addition of forces: In the case of parallel forces the vectors are added as;

– Add the magnitude of force vectors in case of like parallel forces.

– Subtract the magnitude of force vectors in case of unlike parallel forces.

Example:

Head to Tail Rule for Addition of forces: If the forces acting on a body are not parallel to each to other but are making an angle, the forces cannot be simply added as described above. In this case, the forces are added by using head to tail rule of vector addition.

Example: Consider two forces ‘F1‘and ‘F2‘ that are acting on a body such that the force ‘F1‘ is making an angle θ1 with the x-axis and the force F2‘ is making an angle θ2 with x-axis as shown in figure;

In order to add these vectors head to tail rule is followed that is;

1) Sketch the first force ‘F1‘ using the same scale according to selected scale in a given direction.

2) Now place the tail of the second force vector ‘F2‘on the head of the first force vector ‘F1‘in the given direction.

3) Now the resultant force vector ‘FR‘ can be obtained by joining the tail of first force vector ‘F1‘to the head of second force vector ‘F2‘.

4) To determine the magnitude of resultant measure the length of ‘FR‘ and convert it back according to given scale. To determine the direction of the resultant measure the angle of resultant θRwith the x-axis.

                                                    FR = F1 +F2  

Q.3) Define moment of a force. Give its mathematical description and elaborate the factors on which it depends?

Answer: Moment of force: “The turning effect produced in a body about a fixed point due to the applied force is called torque or moment of force”.

Mathematically,

                    Torque = force applied × moment arm

                                    τ = F × d

Torque is a vector quantity and its unit is Newton-meter or Nm.

Factors affecting Torque:

Torque depends upon two factors:

1) Magnitude of applied force (F): Greater the magnitude of force greater will be torque.

2) Magnitude of moment arm (d): "The perpendicular distance between the axis of rotation and the line of the action of force is called the moment arm of the force”.

The longer the moment arm of the force, the greater will be torque.

Example: When we open or close the door, Force ‘F‘ is applied at perpendicular distance ‘d‘ from the axis of rotation as shown in the figure.  Increasing the applied force ‘F‘ or the moment arm ‘d‘ increases the torque ‘τ’. Reducing applied force ‘F‘ or moment arm ‘d‘ decreases torque

Q.4) What is resolution of forces? Explain with an example how forces can be resolved into rectangular components.

Answer: Resolution of Forces: “The process of splitting a force vector into two or more force vectors (component) is called resolution of forces”.

Explanation: For Example, an ice block is being pulled by a boy using rope. We can think of force as tension in the rope. This single force F can be resolved into two components- one directed upwards rightwards along x-axis (Fx) and the other directed upwards along y-axis (Fy) as shown.

Consider the force ‘F‘ in the Cartesian coordinate system represented by line ‘OA’ making an angle θ with the x-axis below.

Draw a perpendicular ‘AB’ on x-axis from ‘A’. According to head to tail rule, ‘OA’ is the resultant vector of OB and BA.

Thus­­­                                                    

                                                OA = OB + BA

From the figure                                          

                                                F = Fx + Fy

Fx and Fy  can be calculated by

Q.5) What is couple? explain with examples.

Answer: Couple: “Two equal and opposite parallel forces acting along different lines on a body constitute a couple”.

The couple does not produce any translation, but only rotation. The resultant force of couple is zero but resultant of a couple is not zero; it is a pure moment. The shortest distance between two couple force is called couple arm

Examples: Forces applied on the steering wheelby both handsis an example of couple. Each hand grips the wheel at points on opposite sides of the shaft. When they apply a force that is equal in magnitude yet opposite in direction the wheel rotates.

Similarly exerting the force on the bicycle pedals, winding up the spring of a toy car, opening and closing the cap of a bottle and turning of a water tap are the examples of couple.

Q.6) Define equilibrium. Explain its types and State the two conditions of equilibrium.

Answer: Equilibrium: “The state of a body in which under the action of several forces acting together there is no change in translation motion, as well as rotational motion, is called equilibrium”

Types of  Equilibrium: The effect of force is to produce change in translational motion and effect of torque is to produce change in rotational motion. Thus the equilibrium is divided into two types.   

1) Static equilibrium: “When a body at rest under the action of several forces acting together and several torques acting on the body is said to be in static equilibrium.”

If there is no change in the state of motion of a body, w.r.t it’s surrounding then it is called static.

When a body is in state of rest and the sum of all forces acting upon it is zero then it is said to be in dynamic equilibrium.

For example, all stationary bodies are in static equilibrium.

2)    Dynamic equilibrium: “When a body is moving at uniform velocity under the action of several forces acting together the body is said to be dynamic equilibrium. If a body is changing its position w.r.t surrounding then it is called dynamic e.g. moving birds, movement of the earth around the sun, running cat and playing football etc.

Dynamic equilibrium, when a body is in state of uniform motion and the resultant of all forces acting upon it is zero then it is said to be in dynamic equilibrium.

For example, Jump by using parachute.

Conditions of equilibrium

There are two conditions of equilibrium which are given below.

1) First condition of equilibrium

2) Second condition of equilibrium

First condition of equilibrium:

Definition: “A body will be in equilibrium if the sum of all the forces acting on the body is zero.”

Mathematically, sum of all forces acting along x-axis should be zero.

Second condition of equilibrium:

Definition: “A body will be in equilibrium if the sum of all the torques acting on the body is zero.”